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If x , y ,z are positive real numbers sh...

If `x , y ,z` are positive real numbers show that: `sqrt(x^(-1)y)dotsqrt(y^(-1)z)dotsqrt(z^(-1)x)=1`

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`sqrt(x^(−1)y)×sqrt(y^(−1)z)×sqrt(z^(−1)x)`
`=sqrt(y/x)×sqrt(z/y)×sqrt(x/z)`
`=sqrt(y/x×z/y×x/z)`
`=1`
Hence proved.
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